**Question:**

A rod is inserted as the core in the current-carrying solenoid of the previous problem.

(a) What is the magnetic intensity $H$ at the centre?

(b) If the magnetization / of the core is found to be $0.12 \mathrm{~A} \mathrm{~m}^{-1}$, find the susceptibility of the material of the rod.

(c) Is the material paramagnetic, diamagnetic or ferromagnetic?

**Solution:**

Given: (a)

Intensity of magnetisation $H=1500 \mathrm{~A} / \mathrm{m}$ As the solenoid and the rod are long and we are interested in the magnetic intensity at the centre, the end effects may be neglected. The sole effect of the rod in the magnetic field of the solenoid is that a magnetisation will be induced in the rod depending on rod magnetic properties. There is no effect of the rod on the magnetic intensity at the centre.

(b) Magnetisation of the core is $I=0.12 \mathrm{~A} / \mathrm{m}$ As we know that

$\mathrm{I}=\mathrm{XH}$...where $\mathrm{X}$ is the susceptibility of the material of the rod.: $\mathrm{X}=\stackrel{\frac{I}{H}}{\therefore}=0.12 / 1500$

$\therefore X=8 \times 10-5$

(c) The material is paramagnetic.